In FIG. 1, a conventional power supply (such as an AC/DC or DC/DC converter) generally includes a rectification unit 1, a boost circuit 2 (such as a conventional power factor correction unit with a boost function) and a switching power conversion unit 3, such that after an input power is passed through the rectification unit 1, and the voltage of the input power is modulated by the boost circuit 2 (such as a conventional power factor correction unit) to a predetermined boost level, and then the power conversion unit 3 converts the boosted input power into an output power, wherein the boost circuit 2 includes a boost unit 21, a switch element 22 and a boost control unit 23. The boost control unit 23 produces a driving signal for controlling an ON or OFF state of the switch element 22, and the ON or OFF state of the switch element 22 determines the charging and discharging cycles of the boost unit 21. The boost control unit 23 adjusts a duty ratio of the driving signal, which controls the ON duration of the driving signal for adjusting the ON time of the switch element 22 to control the voltage of the boost unit 21 and achieve the effect of modulating the boost voltage of the input power. After the power conversion unit 3 has obtained the input power, the boost control unit 23 of the boost circuit 2 adjusts the ON duration of the driving signal to its maximum in the same cycle to enter into the operating state, so that the boost unit 21 boosts to a predetermined voltage level (for example, a boost circuit of a general conventional power supply boosts the voltage over 380V) in the shortest time. In FIG. 2, the boost circuit 2 achieves the boost and modulation effects by continuous high frequency switching, and its operating principle is a prior art. However, the boost circuit 2 produces a large quantity of high frequency driving signals during the boost cycle, and thus the waveform shown in the figure only indicates the rise of an input power 91 and the change of duration of a driving signal 92. In the upper portion of FIG. 2, a voltage waveform of the input power 91 is shown. At the beginning, the voltage of the input power 91 is still different from a boost level 93, such that the driving signal 92 generated by the boost control unit 23 has a maximum ON duration width for modulating the input power to boost to the boost level in the shortest time, and the power supply enters into a standby state or a working state. Until the voltage of the input power 91 reaches the boost level 93, the ON duration of the driving signal 92 is reduced to a normal condition. If the boost control unit 23 uses the maximum ON duration to drive the boost unit 21 for charging, the boost unit 21 will produce a maximum inrush current, which will damage related circuits and components. The circuit will break down easily if high-voltage durable components are not used, but high-voltage durable components incur a high cost and require a larger volume, which are incompliance with the product trend for a low price and a compact size of electronic products. The issue of producing an inrush current when the boost circuit 2 boosts the voltage demands immediate attention and feasible solutions.